We consider the effect of new physics on the branching ratio of B-s -> l(+)l(-)gamma where l = e, mu. If the new physics is of the form scalar/pseudoscalar, then it makes no contribution to B-s -> l(+)l(-)gamma, unlike in the case of B-s -> l(+)l(-)gamma, where it can potentially make a very large contribution. If the new physics is in the form of vector/axial- vector operators, then the present data on B -> (K,K*)l(+)l(-) does not allow a large enhancement for B(B-s -> l(+)l(-)gamma). If the new physics is in the form of tensor/pseudotensor operators, then the data on B -> (K, K*)l(+)l(-) gives no useful constraint but the data on B -> K*gamma does. Here again, a large enhancement of B(B-s -> l(+)l(-)gamma), much beyond the Standard Model expectation, is not possible. Hence, we conclude that the present data on b -> s transitions allow a large boost in B(B-s -> l(+)l(-)) but not in B(B-s -> l(+)l(-)gamma).